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Epsilon Naught – Definition, Value, Derivatives and Uses

Aug 11, 2022

Epsilon Naught Value

Epsilon naught is the permittivity of open space, usually referred to as the electric constant or vacuum permittivity. The Greek alphabet “0” denotes the Epsilon naught value. Another comparable concept is epsilon naught, represented by the symbol “ε”. The permittivity of insulating or dielectric material is measured in units called epsilon.

What is Epsilon Naught?

So, what is epsilon naught? Epsilon naught is the permittivity of open space, represented by the symbol ε0, also known as epsilon zero. It implies that the value of ε0 determines the magnitude of the electromagnetic field in free space. When the permittivity of the medium is high, it will quickly become polarized when introduced to an electric field.


Permittivity can be defined as the measure of the resistance put up to the development of an electric field. The value ε0 specifically describes the permittivity of the vacuum (medium). A vacuum can be classified as the vacant region or space of all substances. 

It was known by several names when originally found. The term “electric constant” is now used to refer to the constant. Earlier, epsilon naught was also referred to as the “dielectric constant of the free space”. At that time, the terms “electric constant” and “dielectric constant” were interchangeable. However, the dielectric constant is employed for defining the value ε/ε0 (a unitless value that indicates the relative permittivity of a medium (substance)in the vacuum.)


Scientists currently even question the name “dielectric constant.” They favor the new word “relative static permittivity” for the “dielectric constant.” In some instances, it is still possible to find manuscripts that refer to the “dielectric constant of open space”.

Did You Know


Dielectric spectroscopy is a technique used to determine a medium’s permittivity. The dielectric characteristics of a medium are calculated in dielectric spectroscopy as a function of the frequency. The data analysis is predicated on the interface between the external field and the sample’s permittivity.

Epsilon Naught Units

The SI and CGS units can be used to define the permittivity of open space (0). The epsilon naught units can be described as follows:

  • Epsilon Naught in SI Unit: Farad per meter or F.m-1
  • Epsilon Naught in CGS Unit: Coulomb squared per Newton meter squared or C2/N.m2

Value of Epsilon Naught

The capacity of the conventional vacuum to accommodate the electric field is known as the permittivity of free space (ε0). Moreover, the value that can be approximated is the one that is well defined:


so, what is the value of epsilon naught, 

ε0 = 8.854187817 × 10-12 F.m-1 (In SI Unit)


additionally, ε0 = 8.854187817 × 10-12C2/N.m2(In CGS Unit)

The formula of Epsilon Naught Value

Epsilon Naught Dimensional Formula = M⁻¹L⁻³T⁴A²


Derivative of Epsilon Naught Formula

According to Coulomb’s Law:

F = (1/4πε₀) q1q2/r²


ε₀ = (1/4πF) q1q2/r²

Dimension formula of F=M¹L¹T⁻²

In the equation, charge = q = IXT = AxT¹, where A stands for electric current.

Therefore, ε₀ = (1/M¹L¹T⁻²)(AT¹xAT¹)/L²

Additionally, ε₀ = M⁻¹L⁻³T⁴A²

Epsilon Naught’s dimensional formula is thus revealed to be M⁻¹L⁻³T⁴A²

What is Permittivity?

Permittivity can be defined as the opposition’s defense against developing an electric field. The electric field can penetrate a vacuum. The constant connects mechanical variables like length and force to the units of electric charge.

Types of Permittivity

There are Three Different Types of Permittivity. These are as follows:

  • The permittivity of a substance: The capacity of a substance to allow an electric current to flow through it is known as permittivity, and the symbol “ε shows it”. It depends on how frequently it occurs, which is ω.
  • The permittivity of open space: The capacity of open space to permit the passage of an electric current is represented by the symbol “ε₀” (permittivity). It is not reliant on frequency ω.
  • Relative Permittivity: Relative permittivity is the ratio of a substance’s permittivity to the permittivity of open space, and the symbol “εᵣ represents it”. It is influenced by frequency ω.

Epsilon Naught is known as the absolute, electric constant, or free space permittivity.

Open Space’s Permittivity

Epsilon Naught represents the permittivity of open space, a region devoid of matter and all fields, including gravitational, electromagnetic, and magnetic ones. In the same way that every material has a unique permittivity, so does open space. The ability of a material to permit the electric current to travel through it is determined by the permittivity of space.

The permittivity of a material or medium varies because each type of material has a unique potential for allowing an electrical field to pass through it; but, in the case of open space, the permittivity is constant because there is no substance or field present. As a result, open space possesses a constant and uniform permittivity.

The Formula of Open Space Permittivity: Using Coulomb’s Law

One can determine the force between two charged objects using Coulomb’s law. The force is inversely related to the square of the space (distance) between the charged bodies and directly related to the products of the charged bodies.

F ∝ q1q2/ r2

Now let’s employ the constant “k” to eliminate the proportionality.

F = kq * q1q2/ r2

Assume the constant ‘k’ is 1 / 4πϵ0. 

F = 1 / 4πϵ0 * q1q2/ r2

Where 0 is the open space’s permittivity.

Derivation of open space permittivity is 0 from Coulomb’s law.


F = 1 / 4πϵ0 ∗ q1q2/ r2


ϵ0 =1 / 4πϵ0 ∗ q1q2/ r2

Considering capacitance

Users are aware that C = 40R is the capacitance of a conductive sphere with radius R is C = 4πϵ0R

Therefore, ϵ0 = C4πR

Did You Know

Ampere was modified in 2019 to refer to a precise number of Coulombs. It led to the vacuum permittivity’s value changing from a mathematically specified value to a measurable value. Additionally, it changed the electron to have a specific charge. Now, the magnetic permeability μ0 is a quantifiable constant as well.

Uses of Epsilon Naught (ε₀)

Now let’s talk about the numerous applications of epsilon naught. One can see why epsilon naught is an essential physics constant by considering the following points.

  • ε0 calculates the force between two electrical charges that are kept apart. It is often used to determine a substance’s dielectric constant. Since there is a vacuum everywhere, the relative permittivity is calculated against the permittivity of open space.
  • ε0 is also used to calculate the capacitance by the formula C = εAD. Where A represents the space between the plates of a capacitor and D is the separation between the plates.
  • Epsilon naught, ε0, can also be used in Gauss’ law, which describes the correlation between the amount of charge contained in an enclosed surface and the proportion of electric flux that goes through that surface. The quantities are directly proportional, and the formula is EdA = 10Qenclosed, where E stands for the electric field, A for the surface’s area, and Qenclsoed for the charge within the surface.
Did You Know

In the quantum physics model, permittivity is characterized by molecular and atomic interactions. The polarized molecules rotate periodically at lower frequencies. Such molecules experience a field that is hostile to the bond when energy is applied. Additionally, the microwave operates on a similar premise. The microwave frequency gives the hydrogen bonds in water energy. 

Water’s dielectric field works to prevent bonds from being broken, and this causes the water to warm up. Thus, the food is cooked using both the energy generated by the microwave and the energy necessary to break the hydrogen bonds. The energy is absorbed in medium frequencies as a component of the responsive molecular movements.


The value of epsilon naught indicates the value of dielectric permittivity in free space. Experts and researchers use the value of epsilon naught to determine the dielectric constant of any substance. The epsilon naught is regarded as the appropriate physical constant representing the absolute dielectric permittivity in the vacuum.

To put it simply, epsilon naught defines the vacuum’s capacity to allow electric field lines to pass through it.

Frequently Asked Questions 

1. Explain the value of epsilon naught?

The permittivity of open space is referred to as Epsilon Naught in physics. Additionally, this numerical value illustrates the maximum allowed electric field in free space or vacuum. Epsilon of water refers to the amount of an electric field that may penetrate or exist in water.

2. What is the value of epsilon naught?

The capacity of the conventional vacuum to accommodate the electric field can be referred to as the permittivity of free space (ε0). Epsilon naught’s approximate value is ε0 = 8.854187817 10-12 F.m-1 (In SI Unit) or ε0 = 8.854187817 10-12 C2/N. m2 (In CGS Unit).

3. What does the term “permittivity of space” mean?

The capacity of the conventional vacuum to allow the electric field is known as the permittivity of free space, or ε0. It is described as the quantity equal to 8.854187817 10-12 F.m-1.

4. What role does epsilon naught play in physics?

It displays the free space’s dielectric permittivity. Additionally, the value of epsilon naught is considered when estimating a material’s dielectric constant.


epsilon naught value


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